RBS is 83 per cent owned by the taxpayer after the government had to step in to rescue the bank following the financial crisis of 2008.

Sir Philip, chairman of RBS since 2009, had been on course to claim 5.17m shares in the financial institution in February, but it is thought he told the bank's remuneration committee it would "not be appropriate" for him to take a £1.4m payout.

Hester was awarded £963,000 last week in a short-term bonus equalling 3.6m shares.

The decision was welcomed by Chancellor George Osborne last night.

"This is a sensible and welcome decision that enables Stephen Hester to focus on the very important job he has got to do, namely to get back billions of pounds of taxpayers' money that was put into RBS," he said.

"It is a shame that a feeble, out of touch David Cameron did not realise he should do the right thing and stand up for the interests of the British people," he said.

"Labour was right to seek a parliamentary vote on this so that the people's voice could be heard. But the debate about fair executive pay and responsible capitalism is only just beginning. We need a government that will tax bankers' bonuses and bring responsibility to the boardroom."

Following Hester's decision to turn down the bonus, shadow business secretary Chuka Umunna said it would be wrong to criticise him for having listened to the public outcry.

"For somebody to listen and respond, we of course wouldn't criticise that he's doing the right thing," he said.

"It's a shame that the government having gone around lecturing shareholders in other large companies to take an active role in bringing about wage restraint chose to sit on its hands in this case and that it took so long for there to be a public clamour and row of this order for the change in position that we have just witness to take place.

"It kind of says something, if you like, of the government talking the talk but not walking the walk."

Hester is still expected to be entitled to another shares bonus that could potentially reach £6.4m based on a long term incentive scheme that is approaching the point at which it can come into effect.

Reported by the Press Association, Chairman of the Financial Services Authority Lord Turner, who said last week that excessive bonuses are "not good for society", will report to the Commons Treasury Committee on RBS tomorrow.

Scottish First Minister Alex Salmond said both the coalition government and previous Labour government shared responsibility for the situation.

"Labour negotiated the very deal with Stephen Hester that they have complained about while the coalition parties huff and puff about shareholder democracy but stand by idly when they carry responsibility for the public shareholding," he said.

"They also have the option of a further tax on bonuses but instead all the Tory rhetoric is on reducing the top rate of tax.

"Collectively the Westminster parties display the complete abdication of responsibility of political parties out of touch with the public of both Scotland and England."

However the move was not welcomed by all politicians. Tory MP Mark Field, whose constituency includes the City of London, claimed Hester had been the victim of a "lynch mob".